Answer:
0.775
Explanation:
The weight of an object on a planet is equal to the gravitational force exerted by the planet on the object:
[tex]F=G\frac{Mm}{R^2}[/tex]
where
G is the gravitational constant
M is the mass of the planet
m is the mass of the object
R is the radius of the planet
For planet A, the weight of the object is
[tex]F_A=G\frac{M_Am}{R_A^2}[/tex]
For planet B,
[tex]F_B=G\frac{M_Bm}{R_B^2}[/tex]
We also know that the weight of the object on the two planets is the same, so
[tex]F_A = F_B[/tex]
So we can write
[tex]G\frac{M_Am}{R_A^2} = G\frac{M_Bm}{R_B^2}[/tex]
We also know that the mass of planet A is only sixty percent that of planet B, so
[tex]M_A = 0.60 M_B[/tex]
Substituting,
[tex]G\frac{0.60 M_Bm}{R_A^2} = G\frac{M_Bm}{R_B^2}[/tex]
Now we can elimanate G, MB and m from the equation, and we get
[tex]\frac{0.60}{R_A^2}=\frac{1}{R_B^2}[/tex]
So the ratio between the radii of the two planets is
[tex]\frac{R_A}{R_B}=\sqrt{0.60}=0.775[/tex]
